# hyperbolicCleanEqn¶

Fluxes and eigensystem for a hyperbolic cleaning system.

\begin{align} \frac{\partial}{\partial t}\left( \begin{array}{c} B_{x} \\ B_{y} \\ B_{z} \\ \psi \\ \end{array} \right) + \nabla\cdot\left( \begin{array}{ccc} \psi & 0 & 0 \\ 0 & \psi & 0 \\ 0 & 0 & \psi \\ \gamma^{2}\,B_{x} & \gamma^{2}\,B_{y} & \gamma^{2}\,B_{z} \\ \end{array} \right) = 0 \end{align}

## Primary Variables (4)¶

1. $$B_{x}$$ x component of vector
2. $$B_{y}$$ y component of vector
3. $$B_{z}$$ z component of vector
4. $$\psi$$ correction potential

0 auxiliary variables

## Parameters¶

gamma (double)

correction potential propagation speed.

## Example¶

An example hyperClean equation block is given below:

<Equation hyperClean>
kind = hyperCleanEqn
gamma = 1.0
</Equation>